Well, let me recomend something else, check asrock mini-itx motherboards with on-board cpu. You can get those for ~150 euros, throw in some ram (~60 euros) and some disk (100euro) + some chasis (Phenom mini-itx for instance, ~100euros). For home server this will work great :)

I am running home server (100% self hosted including emails) with J1900-itx motherboard with 20Tb of disk space (zraid) for years. No need to bother with ps4/5.

Yes, but ps4 is gaming rig and you will have to jailbreak it every reboot. It depends on what you intend to run, raspberry pi 4 and sd card could be just more then enough for some people. Those prices were over the thumb, my motherboard with cpu is there since 2014 and is now $60 while it is more than enough and with going minimal (ram, chasis, disk - with ps4 you will get 1tb at most) you can pull it of under ps4 price. At the end, if you divide those 400 euros by 6 years, you are at price of 5.55 euro / month (not to mention you can reuse chasis and disks when upgrading) and it is low power setup (measured with 4 disks was 33 watts).